As is known in the art, photovoltaic devices operate using a single photon absorption (SPA) process in which a photon with energy equal to or greater than the bandgap of the semiconductor body having a p-n junction generates a single electron-hole (e-h) pair, as illustrated in FIG. 1A. The photon-generated (herein sometimes referred to as “photo-generated”) electron and hole are then collected for electrical power generation using a p-n junction diode. The flow of photo-generated electrons and holes across the p-n junction results in current flow through the body and generation of the voltage across the end terminals at the p and n regions of the body. The photons having energy below the bandgap energy of the semiconductor do not contribute to the generation of e-h pairs. The electric current flowing in the semiconductor body is dependent on the number of photo-generated electrons and holes. The voltage generated across the end terminals is dependent on the bandgap of the semiconductor body. A photon with energy in excess of the bandgap energy will generate an e-h pair wherein the energy excess of the bandgap energy will be eventually lost in form of heat (also known as the phononic loss). The detailed balance limit of efficiency due to all these factors provide the upper limit for energy conversion efficiency from a broad band optical source of energy (such as a hot blackbody radiator like the sun) to electrical energy. This is referred to as the Shockley-Queisser limit. For a single (one bandgap) p-n junction crystalline semiconductor device, the theoretical limiting power efficiency is approximately 31%. With a large number of stacked/tandem p-n junctions with different bandgaps (with each bandgap capturing a small section/range of photon energy from the broad band radiation), the corresponding theoretical limit increases. For a stack of 36 bandgaps, the maximum theoretical efficiency is 72% [S. M. Sze, Physics of Semiconductor Devices. 2nd Edition, Page 798, John Wiley & Sons Inc., New York (1981); W. Walukiewicz, “Semiconductor Materials for Intermediate Band Solar Cells”, GCEP Solar Energy Workshop, 19 Oct. 2004]. By concentrating the sunlight, one could further enhance the conversion efficiency. In September 2013, a solar cell achieved 44.7 percent efficiency with an intensity concentration equivalent to 297 suns, as demonstrated by the German Fraunhofer Institute for Solar Energy Systems [Fraunhofer-Institut fur Solare Energiesysteme ISE, Press Release, 23 Sep. 2013].
In essence, the bandgap of semiconductor single p-n junction devices can be optimized to exhibit maximum conversion efficiency for a specific black-body spectrum (depending on the temperature of the radiator). Efforts to convert a larger portion of the black-body spectrum into electrical power with efficiency exceeding the Shockley-Queisser limit use bodies with multiple bandgaps assembled vertically (such as tandem cells) or laterally (such as in systems with spectrum splitting). Current SPA photovoltaic (PV) processes that convert optical power (electromagnetic radiation) such as light from a blackbody source (such as the sun) or a source of thermal radiation (such as a flare or waste heat from a furnace) into electric power is therefore limited in its energy conversion efficiency by the fundamental Shockley-Queisser limit. Commercially available silicon solar cells that convert sunlight into electric energy exhibit conversion efficiencies approximately 20%; the highest theoretical efficiency for a single p-n junction solar cell device being limited, as noted above is approximately 31%. By increasing the concentration of the intensity of incident sunlight using a concentrator (also known as concentrator photovoltaics or CPV) technology, it is theoretically possible to enhance the efficiency to approximately 37% at an optical concentration ratio of 1000 [S. M. Sze, Physics of Semiconductor Devices. 2nd Edition, Page 798, John Wiley & Sons Inc., New York (1981); G. Gabetta, “High Efficiency Photovoltaic power plants: the II-V compound solar cells, 2011 CESI]. However the light (power per unit area) concentration cannot be increased beyond a certain threshold level without the materials in the body being degraded. Another approach for enhancing the efficiency is by absorbing the broad energy spectrum from black body radiation using a series of devices with semiconductors having different bandgaps. This has been used in the PV industry for creating tandem solar cells with efficiencies close to 40% (using 3 different semiconductors placed on top of each other also known as triple junction cells). However, these devices are very expensive and work efficiently only under specific conditions.
For over four decades, intense research has been dedicated to the development of increasing effective solar cell efficiency by multi junction devices, multiple absorption path solar cells (using impact ionization multiple exciton generation), multiple energy level solar cells (using localized levels or intermediate bands), multiple spectrum solar cells (using up and down conversion of photons), multiple temperature solar cells (using utilization of hot carriers), dilute II-VI oxide semiconductor cells (ZnMnOTe), and solar thermo-photovoltaics (TPV). These SPA techniques include: 1) Stacking different band gap semiconductors to collect broader spectral bands; 2) Optimizing individual p-n junction by strategies to minimize charge carrier (electron and hole) recombination; 3) Optimizing the active region thickness by balancing absorption, non-radiative processes, radiative losses, and carrier diffusion lengths; (4) Other enhancement approaches include: modifying the surface structure of the cell and using multilayer coatings, which are designed to couple light into the structure by interference, and scatter light into oblique angles of the surface trapping weakly absorbed wavelengths; (5) Detailed suggestions have included quantum dots, but their efficiencies have not yet approached traditional methods; (6) Intermediate state cells have been fabricated, but efficiencies are below traditional levels; and (7) Multiple exciton generation via the inverse auger effect has also been demonstrated, but with poor performance in existing devices. The above approaches only provide a sub-set of the criteria that is necessary for accomplishing high efficiency device. An ideal PV device needs to satisfy the following criteria to demonstrate the highest theoretical conversion efficiency: Zero series resistance, Infinite shunt resistance, Zero surface recombination (perfectly passivated surfaces), Zero dislocations or extended defects in the PV material, Extremely high carrier lifetimes (requiring highest quality single crystal), P+I N+ structure (for efficient carrier collection), Perfect anti-reflection (AR) coating plus textured top surface, Back-surface reflector for photon recycling, Back surface field (electric) profile (for carrier confinement), preferably direct bandgap semiconductor (GaP, GaAs, InP, GaSb, CdTe, and so forth), High optical concentration, Low operation temperature. There has been a challenge on multiple fronts in spite of over 4 decades of research to accomplish many of the above criteria.
As is also known in the art, non-linear Two-Photon Absorption (TPA) is a non-linear multi-photon optical process in which two photons (from the incident radiation) each with energy less than the bandgap energy of the semiconductor having identical or different wavelength (or frequencies) are absorbed simultaneously (typically within a nanosecond) in a body whereby an electron in the body is elevated from a lower energy electron state (usually the ground state) to a higher energy electron state as illustrated in FIG. 1B; see papers by: S. Fathpour, K. Tsia and B. Jalali, “Two-Photon Photovoltaic Effect in Silicon”, IEEE Journal of Quantum Electronics, vol. 43, p. 1211, 2007, and B. Jalali; S. Fathpour “Silicon Photonics”, IEEE Journal of Lightwave Technology, vol. 24, p. 460, 2006; M. B. Haeri, S. R. Kingham, and P. K. Milsom, “Nonlinear absorption and refraction in indium arsenide,” J. Appl. Phys. 99 (1), 013514, 2006; and K. W. Berryman and C. W. Rella, “Nonlinear absorption in indium arsenide”, Phys. Rev. B, 55(11), 7148-7154, 1997. The energy difference between the involved lower and upper states is equal to or less than the sum of the energies of each of the two photons as shown in FIG. 1B.
There is another fundamental difference between the nonlinear TPA and the SPA processes. More particularly, the inverse of the absorption coefficient, a, defines the average distance traveled by a photon before it is absorbed by a material. The absorption coefficient describes the photon intensity (power per unit area) as the light travels through the material by the differential equation,
                    d        dz            ⁢              I        ⁡                  (          z          )                      =                  -        α            ⁢                          ⁢              I        ⁡                  (          z          )                      ,where α is the absorption coefficient, and I(z) is the photon beam intensity at location z into the medium; where
  -                        d        dz            ⁢              I        ⁡                  (          z          )                        may be considered as the rate of intensity absorption as the light travels through the body. For photon energy equal to or exceeding the band gap of the semiconductor, the absorption coefficient for the Single Photon Absorption (SPA) process is dependent on the specific semiconductor material and the photon energy. The absorption coefficient is approximately a constant independent of the intensity of the optical beam.
At sufficiently high optical intensities, nonlinear multi-photon processes can dominate absorption. As an example, nonlinear degenerate two photon absorption (TPA) is a special case of nonlinear multi-photon processes. (The term degenerate refers to each photon having the same energy.) In this case, for two photons with each having energy less than the band gap, the nonlinear TPA process combines the photons to elevate charge carriers (electrons) from the valence band to the conduction band.
Unlike the SPA process, in the degenerate TPA process, the optical absorption coefficient (a) of the body is proportional to the optical intensity of the incident light (I) with α=βI, where β is the proportionality constant depending on the materials' properties. A simplified representation for the nonlinear degenerate TPA process can be described by a material dependent nonlinear absorption coefficient, β, which governs the TPA absorption via the simplified equation,
            d      dz        ⁢          I      ⁡              (        z        )              =            -      β        ⁢                  ⁢                            I          2                ⁡                  (          z          )                    .      
Thus the distinguishing feature of degenerate TPA is that the rate of absorption of light by a material depends on the square of the light's intensity. This is different from SPA, where the rate of absorption of light is linear with respect to input light intensity.
The TPA has been used with coherent sources of radiation for a variety of applications including optical power limiters. For optical power limiters, in a material with a strong nonlinear effect, the absorption of light increases with intensity such that beyond a certain input intensity the output intensity approaches a constant value. Such a material can be used to limit the amount of optical power entering a system. This can be used to protect expensive or sensitive equipment such as sensors, can be used in protective goggles, or can be used to control noise in laser beams.
While TPA has been generated by exposing a body to coherent radiation as from a laser, the inventors have recognized providing a photovoltaic system that directly generates electrical power in response to incoherent radiation producing such electric power by nonlinear multi-photon absorption or nonlinear TPA, as for example from sunlight, would result in inexpensive, highly efficient system and method for electric power generation.